Local convergence for a multi-point family of super-Halley methods in a Banach space under weak conditions

Ioannis K. Argyros, and Santhosh George. "Local convergence for a multi-point family of super-Halley methods in a Banach space under weak conditions." Applicationes Mathematicae 42.2-3 (2015): 193-203. <http://eudml.org/doc/280075>.

@article{IoannisK2015,
abstract = {We present a local multi-point convergence analysis for a family of super-Halley methods of high convergence order in order to approximate a solution of a nonlinear equation in a Banach space. Our sufficient convergence conditions involve only hypotheses on the first and second Fréchet derivative of the operator involved. Earlier studies use hypotheses up to the third Fréchet derivative. Numerical examples are also provided.},
author = {Ioannis K. Argyros, Santhosh George},
journal = {Applicationes Mathematicae},
keywords = {super-Halley method; local convergence; nonlinear operator equation; Banach space; Fréchet derivative; numerical example},
language = {eng},
number = {2-3},
pages = {193-203},
title = {Local convergence for a multi-point family of super-Halley methods in a Banach space under weak conditions},
url = {http://eudml.org/doc/280075},
volume = {42},
year = {2015},
}

TY - JOUR
AU - Ioannis K. Argyros
AU - Santhosh George
TI - Local convergence for a multi-point family of super-Halley methods in a Banach space under weak conditions
JO - Applicationes Mathematicae
PY - 2015
VL - 42
IS - 2-3
SP - 193
EP - 203
AB - We present a local multi-point convergence analysis for a family of super-Halley methods of high convergence order in order to approximate a solution of a nonlinear equation in a Banach space. Our sufficient convergence conditions involve only hypotheses on the first and second Fréchet derivative of the operator involved. Earlier studies use hypotheses up to the third Fréchet derivative. Numerical examples are also provided.
LA - eng
KW - super-Halley method; local convergence; nonlinear operator equation; Banach space; Fréchet derivative; numerical example
UR - http://eudml.org/doc/280075
ER -